Professor Lotfi A. Zadeh, the inventor of the current disclosure, is the “Father of Fuzzy Logic”. He first introduced the concept of Fuzzy Set and Fuzzy Theory in his famous paper, in 1965 (as a professor of University of California, at Berkeley). Since then, many people have worked on the Fuzzy Logic technology and science. Dr. Zadeh has also developed many other concepts related to Fuzzy Logic. The last revolutionary one is called Z-numbers, named after him (“Z” from Zadeh), which is the subject of the current invention. That is, the embodiments of the current invention are based on or related to Z-numbers and Fuzzy Logic. The concept of Z-numbers was first published in a recent paper, by Dr. Zadeh, called “A Note on Z-Numbers”, Information Sciences 181 (2011) 2923-2932.
In the real world, uncertainty is a pervasive phenomenon. Much of the information on which decisions are based is uncertain. Humans have a remarkable capability to make rational decisions based on information which is uncertain, imprecise and/or incomplete. Formalization of this capability is a purpose of this invention.
Here are some of the publications on the related subjects:    [1] R. Ash, Basic Probability Theory, Dover Publications, 2008.    [2] J-C. Buisson, Nutri-Educ, a nutrition software application for balancing meals, using fuzzy arithmetic and heuristic search algorithms, Artificial Intelligence in Medicine 42, (3), (2008) 213-227.    [3] E. Trillas, C. Moraga, S. Guadarrama, S. Cubillo and E. Castifieira, Computing with Antonyms, In: M. Nikravesh, J. Kacprzyk and L. A. Zadeh (Eds.), Forging New Frontiers: Fuzzy Pioneers I, Studies in Fuzziness and Soft Computing Vol 217, Springer-Verlag, Berlin Heidelberg 2007, pp. 133-153.    [4] R. R. Yager, On measures of specificity, In: O. Kaynak, L. A. Zadeh, B. Turksen, I. J. Rudas (Eds.), Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications, Springer-Verlag, Berlin, 1998, pp. 94-113.    [5] L. A. Zadeh, Calculus of fuzzy restrictions, In: L. A. Zadeh, K. S. Fu, K. Tanaka, and M. Shimura (Eds.), Fuzzy sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, pp. 1-39.    [6] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
Part I: Information Sciences 8 (1975) 199-249;
Part II: Information Sciences 8 (1975) 301-357;
Part III: Information Sciences 9 (1975) 43-80.    [7] L. A. Zadeh, Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs, Multiple-Valued Logic 1, (1996) 1-38.    [8] L. A. Zadeh, From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions, IEEE Transactions on Circuits and Systems 45, (1999) 105-119.    [9] L. A. Zadeh, The Z-mouse—a visual means of entry and retrieval of fuzzy data, posted on BISC Forum, Jul. 30, 2010. A more detailed description may be found in Computing with Words—principal concepts and ideas, Colloquium PowerPoint presentation, University of Southern California, Los Angeles, Calif., Oct. 22, 2010.
As one of the applications mentioned here in this disclosure, for comparisons, some of the search engines or question-answering engines in the market (in the recent years) are (or were): Google °, Yahoo®, Autonomy, IBM®, Fast Search, Powerset® (by Xerox® PARC and bought by Microsoft®), Microsoft® Bing, Wolfram®, AskJeeves, Collarity, Vivisimo®, Endeca®, Media River, Hakia®, Ask.com®, AltaVista, Excite, Go Network, HotBot®, Lycos®, Northern Light, and Like.com.
Other references on related subjects are:    [1] A. R. Aronson, B. E. Jacobs, J. Minker, A note on fuzzy deduction, J. ACM27 (4) (1980), 599-603.    [2] A. Bardossy, L. Duckstein, Fuzzy Rule-based Modelling with Application to Geophysical, Biological and Engineering Systems, CRC Press, 1995.    [3] T. Berners-Lee, J. Hendler, O. Lassila, The semantic web, Scientific American 284 (5) (2001), 34-43.    [4] S. Brin, L. Page, The anatomy of a large-scale hypertextual web search engine, Computer Networks 30 (1-7) (1998), 107-117.    [5] W. J. H. J. Bronnenberg, M. C. Bunt, S. P. J. Lendsbergen, R. H. J. Scha, W. J. Schoenmakers, E. P. C. van Utteren, The question answering system PHLIQA1, in: L. Bola (Ed.), Natural Language Question Answering Systems, Macmillan, 1980.    [6] L. S. Coles, Techniques for information retrieval using an inferential question-answering system with natural language input, SRI Report, 1972.    [7] A. Di Nola, S. Sessa, W. Pedrycz, W. Pei-Zhuang, Fuzzy relation equation under a class of triangular norms: a survey and new results, in: Fuzzy Sets for Intelligent Systems, Morgan Kaufmann Publishers, San Mateo, Calif., 1993, pp. 166-189.    [8] A. Di Nola, S. Sessa, W. Pedrycz, E. Sanchez, Fuzzy Relation Equations and their Applications to Knowledge Engineering, Kluwer Academic Publishers, Dordrecht, 1989.    [9] D. Dubois, H. Prade, Gradual inference rules in approximate reasoning, Inform. Sci. 61 (1-2) (1992), 103-122.    [10] D. Filev, R. R. Yager, Essentials of Fuzzy Modeling and Control, Wiley-Interscience, 1994.    [11] J. A. Goguen, The logic of inexact concepts, Synthese 19 (1969), 325-373.    [12] M. Jamshidi, A. Titli, L. A. Zadeh, S. Boverie (Eds.), Applications of Fuzzy Logic—Towards High Machine Intelligence Quotient Systems, Environmental and Intelligent Manufacturing Systems Series, vol. 9, Prentice-Hall, Upper Saddle River, N.J., 1997.    [13] A. Kaufmann, M. M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand, New York, 1985.    [14] D. B. Lenat, CYC: a large-scale investment in knowledge infrastructure, Comm.ACM38 (11) (1995), 32-38.    [15] E. H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man—Machine Studies 7 (1975), 1-13.    [16] J. R. McSkimin, J. Minker, The use of a semantic network in a deductive question-answering system, in: IJCAI, 1977, pp. 50-58.    [17] R. E. Moore, Interval Analysis, SIAM Studies in Applied Mathematics, vol. 2, Philadelphia, Pa., 1979.    [18] M. Nagao, J. Tsujii, Mechanism of deduction in a question-answering system with natural language input, in: ICJAI, 1973, pp. 285-290.    [19] B. H. Partee (Ed.), Montague Grammar, Academic Press, New York, 1976.    [20] W. Pedrycz, F. Gomide, Introduction to Fuzzy Sets, MIT Press, Cambridge, Mass., 1998.    [21] F. Rossi, P. Codognet (Eds.), Soft Constraints, Special issue on Constraints, vol. 8, N. 1, Kluwer Academic Publishers, 2003.    [22] G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, N.J., 1976.    [23] M. K. Smith, C. Welty, D. McGuinness (Eds.), OWL Web Ontology Language Guide, W3C Working Draft 31, 2003.    [24] L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353.    [25] L. A. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968), 421-427.    [26] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. on Systems Man Cybernet. 3 (1973), 28-44.    [27] L. A. Zadeh, On the analysis of large scale systems, in: H. Gottinger (Ed.), Systems Approaches and Environment Problems, Vandenhoeck and Ruprecht, Gottingen, 1974, pp. 23-37.    [28] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Part I, Inform. Sci. 8 (1975), 199-249; Part II, Inform. Sci. 8 (1975), 301-357; Part III, Inform. Sci. 9 (1975), 43-80.    [29] L. A. Zadeh, Fuzzy sets and information granularity, in: M. Gupta, R. Ragade, R. Yager (Eds.), Advances in Fuzzy Set Theory and Applications, North-Holland Publishing Co, Amsterdam, 1979, pp. 3-18.    [30] L. A. Zadeh, A theory of approximate reasoning, in: J. Hayes, D. Michie, L. I. Mikulich (Eds.), Machine Intelligence, vol. 9, Halstead Press, New York, 1979, pp. 149-194.    [31] L. A. Zadeh, Test-score semantics for natural languages and meaning representation via PRUF, in: B. Rieger (Ed.), Empirical Semantics, Brockmeyer, Bochum, W. Germany, 1982, pp. 281-349. Also Technical Memorandum 246, AI Center, SRI International, Menlo Park, Calif., 1981.    [32] L. A. Zadeh, A computational approach to fuzzy quantifiers in natural languages, Computers and Mathematics 9 (1983), 149-184.    [33] L. A. Zadeh, A fuzzy-set-theoretic approach to the compositionality of meaning: propositions, dispositions and canonical forms, J. Semantics 3 (1983), 253-272.    [34] L. A. Zadeh, Precisiation of meaning via translation into PRUF, in: L. Vaina, J. Hintikka (Eds.), Cognitive Constraints on Communication, Reidel, Dordrecht, 1984, pp. 373-402.    [35] L. A. Zadeh, Outline of a computational approach to meaning and knowledge representation based on a concept of a generalized assignment statement, in: M. Thoma, A. Wyner (Eds.), Proceedings of the International Seminar on Artificial Intelligence and Man—Machine Systems, Springer-Verlag, Heidelberg, 1986, pp. 198-211.    [36] L. A. Zadeh, Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs, Multiple-Valued Logic 1 (1996), 1-38.    [37] L. A. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems 90 (1997), 111-127.    [38] L. A. Zadeh, From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions, IEEE Trans. on Circuits and Systems 45 (1) (1999), 105-119.    [39] L. A. Zadeh, Toward a perception-based theory of probabilistic reasoning with imprecise probabilities, J. Statist. Plann. Inference 105 (2002), 233-264.    [40] L. A. Zadeh, Precisiated natural language (PNL), AI Magazine 25 (3) (2004), 74-91.    [41] L. A. Zadeh, A note on web intelligence, world knowledge and fuzzy logic, Data and Knowledge Engineering 50 (2004), 291-304.    [42] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)—an outline, Inform. Sci. 172 (2005), 1-40.    [43] J. Arjona, R. Corchuelo, J. Pena, D. Ruiz, Coping with web knowledge, in: Advances in Web Intelligence, Springer-Verlag, Berlin, 2003, pp. 165-178.    [44] A. Bargiela, W. Pedrycz, Granular Computing—An Introduction, Kluwer Academic Publishers, Boston, 2003.    [45] Z. Bubnicki, Analysis and Decision Making in Uncertain Systems, Springer-Verlag, 2004.    [46] P. P. Chen, Entity-relationship Approach to Information Modeling and Analysis, North-Holland, 1983.    [47] M. Craven, D. DiPasquo, D. Freitag, A. McCallum, T. Mitchell, K. Nigam, S. Slattery, Learning to construct knowledge bases from the world wide web, Artificial Intelligence 118 (1-2) (2000), 69-113.    [48] M. J. Cresswell, Logic and Languages, Methuen, London, UK, 1973.    [49] D. Dubois, H. Prade, On the use of aggregation operations in information fusion processes, Fuzzy Sets and Systems 142 (1) (2004), 143-161.    [50] T. F. Gamat, Language, Logic and Linguistics, University of Chicago Press, 1996.    [51] M. Mares, Computation over Fuzzy Quantities, CRC, Boca Raton, Fla., 1994.    [52] V. Novak, I. Perfilieva, J. Mockor, Mathematical Principles of Fuzzy Logic, Kluwer Academic Publishers, Boston, 1999.    [53] V. Novak, I. Perfilieva (Eds.), Discovering the World with Fuzzy Logic, Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg, 2000.    [54] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.    [55] M. K. Smith, C. Welty, What is ontology? Ontology: towards a new synthesis, in: Proceedings of the Second International Conference on Formal Ontology in Information Systems, 2002.
However, none of the prior art teaches the features mentioned in our invention disclosure.